To move up in ranking you will need to be a relatively strategic thinker (in comparison to whomever you are facing). However, the very smart feature of Chess Evolved Online, is that it shows you which spaces can be attacked/moved to. This helps reduce the 'classic Chess' skill needed and enables a faster, strategy focused, more level playing field match.
Please feel free to add any relevant, not previously added strategies. I will start adding pictures as I run across these decks again.
All strategies are adaptable, take your piece collection and try one that looks like it suits your play style. Often, you may even be able to fit multiple strategies into your setup to give you extra options.
General idea: Believe it or not, the classic chess board set up is still very powerful. A few expert or above players I've faced essentially run the normal setup with the pieces upgraded to their tier 2 version. As soon as Bishop and Rooks can reposition diagonally/sideways and knights can move sideways it is very hard to escape the reach of classic+ setup. Queen+ is just scary.
These players are confident at classic chess and use the increased movement to out maneuver and out range opponents.
Variations: You can replace a piece with your favorite new piece from CEO. Portals and ethereal minions can let you get your long range attacking pieces out much faster.
General idea: Starting at Fireball+, these have a good range of 2 both straight ahead and diagonally allowing them to cover each other very effectively. You can use the fireballs on high value minions or champions and try to remove low value pieces safely with your other units; they are relatively cheap but will not make a good trade straight up if your opponent runs all pawns/spiders. Strong area control pieces like Pyromancers, Dryad, or Soulkeepers can take advantage of the protective coverage the fireballs provide to keep minions away.
The main weakness of the fireballs is that they are immobile, but you can use your other units to reposition them. Many ghostly and mage pieces get swap abilities (especially after an upgrade or two); Wizard+ in particular can go crazy with a fireball setup, swapping them all over the place. Placing a Banshee+++ in either corner with a fireball in front of it allows a turn 2 fireball attack on an enemy Lifestone directly ahead, since Lifestones are commonly placed on the edge of the board. Harpy can be used for an even faster combo.
Counters: Strong, cheap minions can push forward aggressively to trade fireballs. Behemoths ignore fireballs entirely. Comet+ and higher can break a huge hole in a firewall from the beginning, and if a frostmage can sneak close enough, he will be able to massively kill fireball. Finally, classic army generally laugh at firewall, not only they have expandables minions, but long range champions like bishop or rook don't bother area denial as they are extremely efficient from the very first row, and can put deadly pins on fireballs.
Enchantress Bomb Edit
General idea: The Enchantress makes a unit immune to melee attack for 2 turns. This effectively means if you can move once and attack your target the next turn, The expensive version is what I lost to today, Enchantress and a Tier 4 Dragon (Dragon+++); the movement range is very large. After a few early swaps of minions the board was too open to stop the immune dragon from attacking the entire half of the board my king was on. The opponent knows what's coming once you enchant your piece with immunity, so normally the king is the main target for the swap to be in your advantage. This tactic works well when paired with a windmage which allows for high mobility, and a slime++ which allows you to start a slime chain.
(Note: As of v0.39, enchanted pieces are unable to attack the enemy king.)
Variations: Alternate versions can swap in Valkyrie or Ninja for early attacks. Haunted Armor plus portal may be pushed by windmage to threaten the opponent early onwards.
Counters: Try to place your King next to a Prince, or in a location not available to be attacked next turn. A Pyromancer or SoulKeeper++ can also be placed into the dragon's move location once you see it enchanted, as only melee attacks can be blocked by the shield. Valkyries can also make it harder to pin down the king in this way. Swapping pieces like Windmage or Wizard also prevent the opponent king from fully being taken.
Minotaur Trap Edit
General idea: Minotaurs are unique in that they're essentially a win condition in their own right. Being able to pull the enemy's King into a vulnerable position lets you threaten an absurdly quick checkmate out of the blue; even if the king manages to retreat to safety, getting the Minotaur into the opponent's back rank lets you make an easy 2-for-1 trade (or even pick up 2 valuable pieces for free, since the 2nd piece teleports the Minotaur back out.) Minotaurs make it very difficult for your opponent to trade, which lets them shut down aggressive trading decks.
There are a couple different ways to use Minotaurs. You can use your Minotaur to provide defensive coverage for obnoxious units like Pyromancer or Ranger, letting you lock down a wide area of the board: anything that captures the protected piece immediately gets taken by the Minotaur, exposing the enemy king to a swift capture. You can also use the Minotaur more aggressively to support a push by other pieces: an attacking piece covered by a Minotaur is virtually uncaptureable unless the opponent wants to expose their king. Just remember that you need to actually have a plan to take the enemy king after he gets swapped, otherwise the opponent will happily sic his king's defenders on your Minotaur for an easy kill and then leisurely walk his king back to safety.
You can also force kills with a Minotaur. The simplest (but most difficult) method is to set up a fork between two enemy champions (or a champion and the king); no matter which one gets saved, the king gets yanked into danger. Enchantresses and Comets are also useful for feeding kills to the Minotaur: an enchanted Minotaur can charge straight into the enemy formation with impunity and a Comet lets you immobilize a victim for the Minotaur to pick off.
Variations: Don't forget to consider an upgraded tier Minotaur if you need more range. Also, a higher tier of summoner can bring opponent pieces into your back line for your Minotaur to take, effectively getting a free king from your opponent.
Counters: Valkyrie can pull the king out of danger, but be sure that the king won't be under attack directly after the minotaur's swap. If it is, then you are forced to pull your king first, and the Minotaur makes a second attack from your king's initial position, landing next to the Valkyrie this time.
General idea: Champion pieces with "extra life" mechanics such as the Gemini, MoonFox, or Phoenix can make very efficient trades with the opponent's pieces. Lifestones can also be used to effectively make any low-to-mid cost champion a multi-life champion, and multiply MoonFoxes to an absurd 4 total lives. When your pieces have more lives than the opponent's, you can afford to aggressively trade and will quickly be able to build up an insurmountable edge.
Counters: All of the "extra life" pieces have ways that they can be permakilled prematurely: magic will prevent MoonFoxes and Phoenixes from spawning, Gemini can be killed before they split, and a MoonFox that doesn't have room to respawn will just die outright. Lifestones can be blocked or destroyed before they have a chance to activate. Most multi-champions are relatively weak and strong minion setups can force them to trade lives for mere minions, diluting their advantage. Minotaurs laugh at aggressive trading strategies.
Windmage++ push Edit
General idea: This is a more complicated strategy. Windmages are very cheap but if you set up a deck to utilize them they are deadly. The best combination I saw had one Windmage++ in the deck. They could then move Samurai out for normal defense and then push it all the way in front of my starting front line. The Samurai worked well since they auto trigger if placed in front of a piece (like a pawn that can't attack back).
Counters: Placing a wisp (or any unit) in the path of a unit about to be pushed will cancel the immediate threat. Especially useful if the enemy has just buffed the unit with enchantress, as the morale cost is now wasted.
Melee Control Edit
General Idea: Inexpensive medium range champions such as the Legionary, Berserker, Medusa, Warrior, etc. give you a great deal of compact area coverage, making it very easy to set up multiple overlapping areas of attack coverage. Unlike line-movers, area melee champions can very easily leapfrog each other to make a mutually supported advance, and can easily set up double and triple area coverage making attacks very difficult. These pieces tend to be relatively cheap which makes it very painful for more expensive pieces to trade. This also frees up a lot of points for you to spend elsewhere, making it easy to afford strong minions with even more area coverage, or a single point sink champion like a Dragon or Queen to clean up after your warrior hordes have thinned out the enemy ranks.
Variations: Because it's relatively inexpensive, it's very easy to take 2-6 melee champions and use them as backup for other strategies. With the release of v0.50, it is also plausible to use Patience while stalling with other pieces until the champion can attack. Another interesting tactic is to attempt to advance multiple minions at once forward with Hoplite, however, this is slow and can be difficult to succeed.
Counters: Ranged and magical units don't care about your overlapping attack coverage and can safely snipe your melee champions regardless of how many spears you have pointed at them. If you have ways of slipping past their formation using enchantment, pushes, or even just outrunning them with long range line movers, their relatively low speed makes it hard for melee champions to catch up.
Magic Control Edit
General Idea: Magical attackers are a formidable defensive tool. Since they can zap away enemies without having to move, it doesn't really matter how well your opponent covers their attackers, they still can't make any headway against your magic pieces. Pyromancers and upgraded Rangers working in mutually supporting pairs are extremely difficult to take out safely, especially since you can park other more expendable pieces in their attack area knowing that anything that attacks into them is going to get zapped. You can even use a layer of Archers in front for even more ranged defense.
Variations: Soulkeepers are another strong magic defender. For the more adventurous, Frost Mages and Poison Mages offer fantastic range and coverage although their magic is much weaker. Necromancers and Liliths work as a budget option but their magical attacks are only usable against minions.
Counters: Antimages are completely immune to magic and ranged attacks, although they're fairly awful so you're unlikely to see them and can easily play around them even if you do. Most magical/ranged attackers are very expensive for their limited coverage, so long range pieces that can force trades can whittle your defensive wall down very easily--and your magic attackers are much more vulnerable once they lose their backup and are fighting on their own.
General Idea: With heavy pressure on one important part of the board (center or corner), many attackers try to control the area. Strong pieces such as bishop, rook, and perhaps even queen use their infinite direction attack to be able to advance pieces forward, especially with ghost or phantasm in front in order to establish the control of the area. Control over the corner can also allow promotions, especially with powerful units such as princess or bat, if enough attackers force the opponents out of the area. A lot of players who use Rush choose to use Ghast as well since they can instantly force more pressure with a trade near the place they wish to conquer.
Variations: Some variations have bombers that get rid of minions so that the champions can attack. It is also possible to use Harpy to push minions forward (usually spearman) and quickly concentrate forces on the corner, however, beware that Harpy has more limited range than Rook and has the weakness of the spot directly in front of it.
Counters: With Dryad, Freezemage, Medusa and other stall units, it is difficult for Rush to usually beat magic. Powerful attackers with infinite direction also trade poorly with defensive units such as legionary and behemoth. In addition, as time goes on the Rusher's advantage grows poor since ghosts do not trade well with minions after the main minion attackers die off. The Rusher's defense grows weak if the defender is able to stall long enough.
Morale Drain Edit
General Idea: Using at least one vampire, this setup tries to get a morale advantage with fair trades (such as legionary) and being able to offset morale lost that comes with powerful minions such as militia or reaver. Over the course of the long game, even a checkmate might not be necessary since vampire's prowess might allow it to take a low morale unit and still win.
Variations: Some variations use Lich as well to offer bonus minions, and lifestone may be used with legionary-- even if they are taken, vampire offsets the normally unfair trade. It is also plausible to use beacon or portal to give vampire mobility.
Counters: Vampire has terrible mobility, and due to their expense they are likely to get forked or trapped in a location. These decks are also usually slow so magic offers a great amount of control over these setups.